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A214444 Arithmetic mean of next a(n) successive squares is prime. 1
7, 5, 7, 5, 7, 5, 151, 29, 31, 5, 7, 101, 35, 25, 7, 5, 7, 5, 7, 5, 35, 53, 7, 25, 35, 25, 43, 5, 35, 65, 7, 65, 91, 17, 7, 65, 83, 13, 59, 173, 7, 25, 11, 13, 7, 17, 7, 25, 11, 17, 7, 65, 43, 61, 35, 17, 79, 53, 23, 29, 11, 29, 35, 101, 7, 17, 11, 29, 35, 5, 35, 25, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Corresponding primes (and arithmetic means):

13, 83, 229, 443, 733, 1091, 14221, 40471, 53441, 62003, 65029, 96331, 142231, 165701, 178933, 184043, 189229, 194483, 199813, 205211, 223831, 267523, 299213, 317021, 351751, 388181, 431803, 463763, 491503, 564353, 619373

Conjecture: for some k and x, a(n)=A214451(n+x) for n>k.

LINKS

Table of n, a(n) for n=1..73.

EXAMPLE

(0+1+4+9+16+25+36)/7 = 13, so a(1)=7. The next set of successive squares with prime arithmetic mean: (7^2 + 8^2 + 9^2 +100 + 11^2)/5 = 83, so a(2)=5.

CROSSREFS

Cf. A000040, A000290, A214442, A214451.

Sequence in context: A178988 A163505 A021136 * A194657 A230163 A143297

Adjacent sequences:  A214441 A214442 A214443 * A214445 A214446 A214447

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Jul 18 2012

STATUS

approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)